Heaven (tenggeri) functioned as a political, ideological justification for Mongol conquest, rather than an initial religious inspiration. Not so much holy wars as a method of political legitimization.
Language used in Secret History evokes Chinese concept of tian and Mandate of Heaven, as well as potentially broader syncretic influences from peoples across Mongol empire.
references
We find in [The Secret History of the Mongols] their models of political legitimization at the time of the conquests, in particular the concept of “Heaven” (tenggeri). The first paragraph begins:
The origin of Činggis Qan. At the beginning there was a blue-grey wolf, born with his destiny ordained by the Heaven above. His wife was a fallow doe. They came crossing the Tenggis.(2) After they had settled at the source of the Onan River on Mount Burqan Qaldun, Batačiqan was born to them.
(2: Lit. “the Sea” or fig. “a large body of water” such a great lake, possibly the Baikal, see Igor de Rachewiltz, Secret History I:1, n. 1.)
The “force of Heaven” assists him in his conquests. Heaven grants him and his successors his protection, as is attested in the diplomatic documents. But while the khan’s success is explained by the support of the “Heaven Above,” he has not in fact received any order to conquer the world in the name of the tenggeri. The Secret History mentions Heaven’s mandate to Genghis Khan only once, in words spoken by the shaman Kököchü (Teb Tenggeri). The context is to rule over the Mongol ulus, i.e. the steppe nomads and not over the whole world. The references to Heaven in the Secret History do not show that Genghis Khan’s foundation of the Mongol empire was due to a heavenly decree. Rather, they serve primarily to retrospectively legitimize a human act, but some researchers pointed out a religious inspiration of Mongol expansion.
These expressions evoke the heaven (tian) of Chinese representations, in particular the “son of the heaven” (tian zi), associated with the emperors of China. Yüan specialists have seen in the tenggeri of the Mongols, and also of the ancient Turks, an influence of the Chinese ideas on the representations of the steppes peoples, see particularly Igor de Rachewiltz […]. Chen Sanping has suggested a new hypothesis as to the origins of the concept. He proposes a synthesis of Altaic, Iranian and Chinese influences in the Turkic and Mongol concepts of Heaven […].
⤷ The Mongol Empire Between Myth and Reality, Denise Aigle